Euler characteristic of crepant resolutions for a certain class of modular quotient singularitiesMPIM

by Linghu Fan (University of Tokyo)

Wednesday Sep 24, 2025, 2:00 PM → 3:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Conference Room (Max Planck Institute for Mathematics)

Extra talk (MPIM conference room, 1st floor!)

From the perspective of McKay correspondence, the Euler characteristic of crepant resolutions of quotient singularities, associated with given finite groups and their (special linear) actions, is an important geometric invariant, which is usually conjectured to be related with certain algebraic invariants of the groups. Over the complex numbers, Batyrev's theorem provides such a relation, of which the direct analogue fails in positive characteristic for the modular case. In this talk, after introducing some background on this topic, we study the Euler characteristic of crepant resolutions for modular groups with a certain semidirect product structure, by considering the wild McKay correspondence as a counting problem of coverings. Based on this result, we propose a conjectural version of Batyrev's theorem in positive characteristic.